An interesting point about grid cells is the lack of influence of external sensory data (for example, visual data) on the activity of cells of that type. Grid cells work only on information about the animal's own movements[1]}.
Thus the mechanism of grid cells can be considered as the assignment of equivalence classes on the set of available controls. I.e. being at A, the animal can reach location B, performing different sequences of movements. The fact that they all lead to the same outcome, unifies them into an outcome equivalence class.
